Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 383
... highway . ( Is this reasonable ? ) If the number of cars in the transition region is always small , show that 393 = 292 . What happens to cars as they go from a two - lane highway into a three - lane highway and vice versa ? 82.6 ...
... highway . ( Is this reasonable ? ) If the number of cars in the transition region is always small , show that 393 = 292 . What happens to cars as they go from a two - lane highway into a three - lane highway and vice versa ? 82.6 ...
Page 384
... highway will develop . ) Consider the two highways in Fig . 82-17 , one which has a bottleneck in which for some distance the road is reduced from three to two lanes : ( 1 ) ( 2 ) Figure 82-17 . Compare highways ( 1 ) and ( 2 ) with the ...
... highway will develop . ) Consider the two highways in Fig . 82-17 , one which has a bottleneck in which for some distance the road is reduced from three to two lanes : ( 1 ) ( 2 ) Figure 82-17 . Compare highways ( 1 ) and ( 2 ) with the ...
Page 389
... highway . 84.2 . Show that the neighboring parabolic characteristics of Sec . 84 first intersect at the same time as the first traffic shock occurs without entrances or exits . Show that the ... Highway Entrance A HIGHWAY ENTRANCE 389*
... highway . 84.2 . Show that the neighboring parabolic characteristics of Sec . 84 first intersect at the same time as the first traffic shock occurs without entrances or exits . Show that the ... Highway Entrance A HIGHWAY ENTRANCE 389*
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude applied approximation Assume calculated called cars characteristics conservation Consider constant continuous corresponding curve decreases density wave depends derived described determine differential equation discussed distance dx dt dx/dt energy equal equilibrium population equilibrium position equivalent example exercise expression Figure force formula friction function given growth rate hence highway illustrated increases indicate initial conditions integral intersect isoclines known length light limit linear manner mass mathematical model maximum measured method motion moving nonlinear number of cars observer obtained occurs oscillation partial differential equation pendulum period phase plane Pmax possible problem region result road satisfies shock Show shown in Fig simple sketched sketched in Fig slope solution solve species spring spring-mass system stable straight line Suppose tion traffic density traffic flow trajectories Umax unstable valid variables yields zero